Welcome to the Dynamical System Group at UFG



The Dynamic Systems Group of UFG, registered in the Directory of Research Groups/CNPq since 2000, is dedicated to the study of the dynamics of vector fields and differential equations from differential geometry.
 
The main focus is the development of the Qualitative and Geometric Theory of Differential Equations, with the main objects of study being smooth or piecewise smooth vector fields, implicit differential equations and fuzzy systems.
 
Differential equations from geometry deal with special curves on surfaces (main curvature lines, asymptotic lines, Darboux curves, median lines) and other issues relating to dynamics and geometry.
 
In the case of smooth or zoned vector fields, we work on the study of global and local dynamics and still following the Thom-Smale program, ie, firstly that subclass constituted by the structurally stable vector fields is studied and then the stability of families to k-parameters, with k=1,2,... We study the existence of minimal sets such as limit cycles and the persistence of homoclinic orbits, as well as the existence of chaotic regimes and other aspects of topological dynamics.
 
In fuzzy dynamic systems, results are sought that can characterize the dynamics in the fuzzy context, using the theory of fuzzy differential inclusions or Zadeh's extension.
In addition to the bibliographical production, the training of qualified human resources is continually sought, as the group guides students in the following modalities: scientific initiation, master's and doctorate in mathematics.

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